Mobile devices have increasingly been used to run multimedia applications which are extremely downlink-intensive. The conventional rate adaptive and/or margin adaptive approach for radio resource allocation may result in unnecessary energy consumption on mobile devices, which will not be energy efficient for mobile multimedia applications. In this paper, we develop an energy adaptive approach and design an energy-efficient downlink resource allocation scheme to support multimedia applications. The objective is to minimize the total energy consumption of mobile devices for data reception while meeting the data rate requirements at mobile devices and the transmit power constraint at the base station. We show that the optimization problem is $\mathcal {NP}$<alternatives><inline-graphic xlink:type="simple" xlink:href="pang-ieq1-2369016.gif"/> </alternatives>-hard and then propose an efficient algorithm that has a provable performance guarantee under a certain condition. We have conducted extensive simulations to evaluate the efficacy of the proposed algorithm and our results provide useful insights into the design of energy-efficient resource allocation for wireless systems.